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Rémi Tailleux

Abstract

In this paper, two new quasi-neutral density variables—generalized patched potential density (GPPD) and thermodynamic neutral density γ T—are introduced, which are showed to approximate Jackett and McDougall empirical neutral density γ n significantly better than the quasi-material rational polynomial approximation γ a previously introduced by McDougall and Jackett. In contrast to γ n, γ T is easily and efficiently computed for arbitrary climatologies of temperature and salinity (both realistic and idealized), has a clear physical basis rooted in the theory of available potential energy, and does not suffer from nonmaterial effects that make γ n so difficult to use in water masses analysis. In addition, γ T is also significantly more neutral than all known quasi-material density variables, such as σ 2, while remaining less neutral than γ n. Because unlike γ n, γ T is mathematically explicit, it can be used for theoretical as well as observational studies, as well as a generalized vertical coordinate in isopycnal models of the ocean circulation. On the downside, γ T exhibits inversions and degraded neutrality in the polar regions, where the Lorenz reference state is the furthest away from the actual state. Therefore, while γ T represents progress over previous approaches, further work is still needed to determine whether its polar deficiencies can be corrected, an essential requirement for γ T to be useful in Southern Ocean studies, for instance.

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Rémi Tailleux

Abstract

Actual energy paths of long, extratropical baroclinic Rossby waves in the ocean are difficult to describe simply because they depend on the meridional-wavenumber-to-zonal-wavenumber ratio τ, a quantity that is difficult to estimate both observationally and theoretically. This paper shows, however, that this dependence is actually weak over any interval in which the zonal phase speed varies approximately linearly with τ, in which case the propagation becomes quasi-nondispersive (QND) and describable at leading order in terms of environmental conditions (i.e., topography and stratification) alone. As an example, the purely topographic case is shown to possess three main kinds of QND ray paths. The first is a topographic regime in which the rays follow approximately the contours f /hαc = a constant (αc is a near constant fixed by the strength of the stratification, f is the Coriolis parameter, and h is the ocean depth). The second and third are, respectively, “fast” and “slow” westward regimes little affected by topography and associated with the first and second bottom-pressure-compensated normal modes studied in previous work by Tailleux and McWilliams. Idealized examples show that actual rays can often be reproduced with reasonable accuracy by replacing the actual dispersion relation by its QND approximation. The topographic regime provides an upper bound (in general a large overestimate) of the maximum latitudinal excursions of actual rays. The method presented in this paper is interesting for enabling an optimal classification of purely azimuthally dispersive wave systems into simpler idealized QND wave regimes, which helps to rationalize previous empirical findings that the ray paths of long Rossby waves in the presence of mean flow and topography often seem to be independent of the wavenumber orientation. Two important side results are to establish that the baroclinic string function regime of Tyler and Käse is only valid over a tiny range of the topographic parameter and that long baroclinic Rossby waves propagating over topography do not obey any two-dimensional potential vorticity conservation principle. Given the importance of the latter principle in geophysical fluid dynamics, the lack of it in this case makes the concept of the QND regimes all the more important, for they are probably the only alternative to provide a simple and economical description of general purely azimuthally dispersive wave systems.

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Rémi Tailleux

Abstract

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ultimately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a nonlinear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

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Lenka Novak and Rémi Tailleux

Abstract

The possibility of constructing Lorenz’s concept of available potential energy (APE) from a local principle has been known for some time, but it has received very little attention so far. Yet the local APE density framework offers the advantage of providing a positive-definite local form of potential energy, which, like kinetic energy, can be transported, converted, and created or dissipated locally. In contrast to Lorenz’s definition, which relies on the exact from of potential energy, the local APE density theory uses the particular form of potential energy appropriate to the approximations considered. In this paper, this idea is illustrated for the dry hydrostatic primitive equations, whose relevant form of potential energy is the specific enthalpy. The local APE density is nonquadratic in general but can nevertheless be partitioned exactly into mean and eddy components regardless of the Reynolds averaging operator used. This paper introduces a new form of the local APE density that is easily computable from atmospheric datasets. The advantages of using the local APE density over the classical Lorenz APE are highlighted. The paper also presents the first calculation of the three-dimensional local APE density in observation-based atmospheric data. Finally, it illustrates how the eddy and mean components of the local APE density can be used to study regional and temporal variability in the large-scale circulation. It is revealed that advection from high latitudes is necessary to supply APE into the storm-track regions, and that Greenland and the Ross Sea, which have suffered from rapid land ice and sea ice loss in recent decades, are particularly susceptible to APE variability.

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Antoine Hochet and Rémi Tailleux

Abstract

have proposed a new theoretical framework for studying ocean heat uptake in potential temperature coordinates. One important step in their derivations requires understanding the temporal changes of the volume of water V with temperature greater than some value, which they write as the sum of two terms. The first one is due to the surface freshwater fluxes and is well defined, but the second one—attributed to the volume fluxes through the lower boundary of the domain—is given no explicit expression. What the authors mean exactly is unclear, however, because in the incompressible Boussinesq approximation, the use of a divergenceless velocity field implies that the sum of the volume fluxes through any kind of control volume must integrate to zero at all times. In this comment, we provide two alternative explicit mathematical expressions linking the volume change of to the diabatic sources and sinks of heat that clarify their result. By contrasting approach with that for a fully compressible ocean, it is concluded that the volume considered by is best interpreted as a proxy for the Boussinesq mass M 0 = ρ 0 V, where ρ 0 is the reference Boussinesq density. If V were truly meant to represent volume rather than a proxy for the Boussinesq mass, the Boussinesq expression for dV/dt would have to be regarded as inaccurate because of its neglect of the volume changes resulting from mean density changes.

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Rémi Tailleux and James C. McWilliams

Abstract

In layered models of the ocean, the assumption of a deep resting layer is often made, motivated by the surface intensification of many phenomena. The propagation speed of first-mode, baroclinic Rossby waves in such models is always faster than in models with all the layers active. The assumption of a deep-resting layer is not crucial for the phase-speed enhancement since the same result holds if the bottom pressure fluctuations are uncorrelated from the overlying wave dynamics.

In this paper the authors explore the relevance of this behavior to recent observational estimates of “too-fast” waves by Chelton and Schlax. The available evidence supporting this scenario is reviewed and a method that extends the idea to a continuously stratified fluid is developed. It is established that the resulting amplification factor is at leading order captured by the formula,
i1520-0485-31-6-1461-eq1
where C fast is the enhanced phase speed, C standard the standard phase speed, Φ1(z) is the standard first mode for the velocity and pressure, and H 0 is the reference depth serving to define it. In the case WKB theory is applicable in the vertical direction, the above formula reduces to
i1520-0485-31-6-1461-eq2
where Nb is the deep Brunt–Väisälä frequency and N its vertical average.

The amplification factor is computed from a global hydrographic climatology. The comparison with observational estimates shows a reasonable degree of consistency, although with appreciable scatter. The theory appears to do as well as the previously published mean-flow theories of Killworth et al. and others. The link between the faster mode and the surface-intensified modes occurring over steep topography previously discussed in the literature is also established.

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Rémi Tailleux and James C. McWilliams

Abstract

The influences of topography on the propagation, spatial patterns, and amplitude variations of long baroclinic Rossby waves are investigated with a wind-forced, two-layer model above a midocean ridge. With steep topography the evolution equation for the baroclinic mode is shown to differ from that for a flat bottom in several ways: 1) The phase speed is systematically faster by the factor H/H 2, where H is the total ocean depth and H 2 is the lower layer thickness, though the propagation remains westward and nearly nondispersive; 2) an effectively dissipative transfer to the barotropic mode occurs whenever the baroclinic mode is locally parallel to f/H contours, where f is the Coriolis frequency; and 3) the wind-forced response is amplified in proportion to the topographic steepness, (f/H)(dH/dx)/(df/dy), for a longitudinally varying topography, which can be a large factor, but the amplification is only by the modest factor H/H 2 for a latitudinally varying topography. Effects 2 and 3 are the result of energy exchanges to and from the barotropic mode, respectively. Effect 3 causes freely propagating, baroclinic Rossby waves to be generated west of the ridge. These effects collectively cause distortions of the baroclinic wave pattern as it traverses the ridge. These effects account qualitatively for several features seen in altimetric measurements in the vicinity of major topographic features: an increase in variance of baroclinic signals on the west side, an enhanced phase speed overall (compared to flat-bottom waves), and an abrupt change in the phase speed at midocean ridges.

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Willem P. Sijp, Jonathan M. Gregory, Remi Tailleux, and Paul Spence

Abstract

A key idea in the study of the Atlantic meridional overturning circulation (AMOC) is that its strength is proportional to the meridional density gradient or, more precisely, to the strength of the meridional pressure gradient. A physical basis that would indicate how to estimate the relevant meridional pressure gradient locally from the density distribution in numerical ocean models to test such an idea has been lacking however. Recently, studies of ocean energetics have suggested that the AMOC is driven by the release of available potential energy (APE) into kinetic energy (KE) and that such a conversion takes place primarily in the deep western boundary currents. In this paper, the authors develop an analytical description linking the western boundary current circulation below the interface separating the North Atlantic Deep Water (NADW) and Antarctic Intermediate Water (AAIW) to the shape of this interface. The simple analytical model also shows how available potential energy is converted into kinetic energy at each location and that the strength of the transport within the western boundary current is proportional to the local meridional pressure gradient at low latitudes. The present results suggest, therefore, that the conversion rate of potential energy may provide the necessary physical basis for linking the strength of the AMOC to the meridional pressure gradient and that this could be achieved by a detailed study of the APE to KE conversion in the western boundary current.

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Lenka Novak, Maarten H. P. Ambaum, and Rémi Tailleux

Abstract

The North Atlantic eddy-driven jet exhibits latitudinal variability with evidence of three preferred latitudinal locations: south, middle, and north. Here the authors examine the drivers of this variability and the variability of the associated storm track. The authors investigate the changes in the storm-track characteristics for the three jet locations and propose a mechanism by which enhanced storm-track activity, as measured by upstream heat flux, is responsible for cyclical downstream latitudinal shifts in the jet. This mechanism is based on a nonlinear oscillator relationship between the enhanced meridional temperature gradient (and thus baroclinicity) and the meridional high-frequency (periods of shorter than 10 days) eddy heat flux. Such oscillations in baroclinicity and heat flux induce variability in eddy anisotropy, which is associated with the changes in the dominant type of wave breaking and a different latitudinal deflection of the jet. The authors’ results suggest that high heat flux is conducive to a northward deflection of the jet, whereas low heat flux is conducive to a more zonal jet. This jet-deflecting effect was found to operate most prominently downstream of the storm-track maximum, while the storm track and the jet remain anchored at a fixed latitudinal location at the beginning of the storm track. These cyclical changes in storm-track characteristics can be viewed as different stages of the storm track’s spatiotemporal life cycle.

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